Functional magnetic resonance imaging (FMRI) is one of the most widely used methods for studying brain function. FMRI makes it possible to perform dynamic imaging of the brain under a broad range of experimental paradigms. This imaging modality will play a central role in deciphering cerebral function into the foreseeable future. Measured fMRI signals consist of a task-dependent hemodynamic response (BOLD signal), low frequency stochastic physiologic fluctuations, scanner background noise, signal drift and motion artifact. Data from fMRI studies represent complex spatio-temporal time-series measured often across several subjects under highly structured experimental protocols. To unlock the subtleties of brain function many experiments require multiple subjects to perform multiple cognitive or behavioral tasks. Statistical methods that are completely faithful to all the intricacies of the fMRI biophysics and the nuances of the experimental designs are not available. The development of such techniques is an active area of statistics and signal processing research. Therefore, the specific aims of this study are to: 1. Formulate, for the analysis of multiple task experiments that use either block or event-related designs, statistical models and model fitting methods that describe accurately the spatio-temporal features of fMRI data. (Multiple Task Data Analysis). 2. Develop models and model fitting methods that accurately describe between and within subject variation in fMRI data. (Multiple Subject Data Analysis). 3. Test our statistical methods in actual and simulated fMRI studies by: a) implementing reliable, numerically efficient computer algorithms for multiple task and multiple subject experiments that can be disseminated to investigators using fMRI; b) comparing our methods directly with the current fMRI data analysis gold standard SPM in simulated and actual data; c) using the methods to analyze actual fMRI studies including investigations of brain networks involved in memory formation, effects of pharmacologic agents on memory formation and language pathology in schizophrenia , that employ both multiple task and multiple subject designs. The project will use the newly developed statistical discipline of functional data analysis (FDA) to define appropriate spatio-temporal random effects models for fMRI data studies. Spatially-regularized maximum likelihood algorithms will be used to fit these models to actual image data series using both C and Matlab. Methods will be disseminated on the web with documentation to ensure ready access to functional imaging and neuroscience researchers. The long-term objectives of the project are to develop and make available to researchers the most up-to-date statistical methods for functional imaging data analysis based on the current understanding of fMRI biophysics and current advances in statistical signal processing.